1. Field of the Invention
The present invention relates to a system for error correction in digital transmissions, and more specifically, to such a system using the so-called Reed Solomon encoding/decoding techniques.
2. Description of the Prior Art
Error correction coding theory in digital transmissions using the so-called Reed Solomon encoding/decoding techniques is well known in the field. See, e.g., W. W. Peterson and E. J. Weldon Jr., "Error Correcting Codes" 2d Ed., The MIT Press, 1972. Such error correction provides for the protection of a transmitted symbol stream from the errors introduced by the transmission channel. This technique foresees the association of each block of k information symbols, generated by the data source, with n-k redundancy symbols selected according to a relation specified in the following description.
The n symbols obtained in this manner are transmitted by the channel characterized by a certain error probability. On the reception side, using the analysis of received symbols and limited by the code correction capacity, the positions of eventual errors introduced by the channel can be located and the originally transmitted information is reconstructed. Visualizing the concept, FIG. 1 shows a conventional system in which the symbols represent the functional blocks (Bxx) and signals (Sxx), and are as follows:
B11) is a data source SO in the form of symbols having a length of m bit in time-serial succession;
S11) is generated by SO, and is the input signal towards the encoder CODIF that is now divided in blocks of k symbols;
B12) is the encoder CODIF that adds n-k redundancy symbols to each input block;
S12) is the signal generated by the encoder CODIF that is now formed with blocks of n symbols;
B13) is a scheme of the transmission channel CT, whereby the transmitted blocks are submitted to errors with a certain probability;
S13) indicates the received symbols that can be considered as an overlapping of the original transmitted symbols and symbols introduced from the channel CT;
B14) is the block DEC that, executes the analysis of received words and, limited to the correction capacity of the code, establishes the positions and the amplitudes of the errors introduced by the channel CT;
S14) is the signal that indicates the error position;
S15) is on its turn the signal that holds the information related to the error amplitude;
B15) is the function block delay that introduces a suitable delay for allowing the correct synchronization of operations;
S16) is the signal that coincides with the signal S13 suitably delayed;
B16) is the block CORR that reconstructs the original information transmitted according to signals S14, S15;
S17) is the sequence of symbols obtained correcting the errors and coinciding with S12;
B17) is the EXTRACTION block of the useful information.
The applications of this technique allow corrections of up to "t" received wrong symbols in a block of n symbols, where t is equal to: t=(n-k)/2 with the preceding definition of parameters. The algorithms used for the association of redundancy symbols to the information symbols in transmission and for decoding the eventual positions of errors in reception are well-known and are described in a general mathematical form in the technical literature.
A brief review of a known application of the Reed Solomon corrections technique should be helpful. Briefly the theoretical basis of this technique applied, e.g., to the case of symbols having a length of m bits, can be described as follows:
Given a generical sequence of L symbols b0, b1, b2, . . . bL-1, it can be associated univocally with a polynomial of degree L-1: ##EQU1##